Time, fuel, and distance calculations

This element is the arithmetic of cross-country planning. The DPE hands you a chart and POH and watches you compute the numbers for a real or hypothetical leg — and they want to hear you walk the math, not just see the answer.

Distance → True course → TAS → wind correction → TH and GS → variation → MH → deviation → CH → ETE → ETA → fuel (taxi + climb + cruise + descent + reserve). The flow is mechanical; the discipline is showing every step.

True course to compass heading

The TVMDC sequence converts what you measured on the chart into what you'll fly on the compass:

• True course (TC) — measured with a plotter from a meridian along the route line on the sectional
• True heading (TH) — TC ± WCA (wind correction angle). Wind from the left → subtract; wind from the right → add
• Magnetic heading (MH) — TH ± variation, read from isogonic lines on the sectional. East is least, west is best — east variation subtract, west variation add
• Compass heading (CH) — MH ± deviation, from the aircraft's compass deviation card (usually < 5°)

Variation is geographic (where you're flying); deviation is aircraft-specific (which compass you're using).

TH 310°, variation 10°E → MH 300°. Deviation card shows +2° at 300 → CH 302°.

TAS and groundspeed from winds

True airspeed (TAS) is IAS corrected for non-standard density:

• From the POH cruise table at altitude, RPM, and OAT, or
• Rule of thumb: TAS ≈ IAS + 2% per 1,000 ft above sea level

IAS 100 KT at 7,500 MSL → TAS ≈ 115 KT.

Wind correction uses TAS, wind direction/speed, and true course (E6B or electronic equivalent):

• Direct headwind: WCA = 0°, GS = TAS − wind
• Direct tailwind: WCA = 0°, GS = TAS + wind
• Quartering or crosswind: E6B gives WCA and GS

Course 320°, wind 270 at 20, TAS 115 → WCA ≈ 10° left, TH 310°, GS ≈ 100 KT.

Pre-loaded with the worked example above. Adjust any of the four inputs to see the WCA, TH, and GS recompute live. Toggle "Show drift" to reveal the red dashed trace — that's where you'd end up flying TC without correcting for wind. The angle between TC and TH IS the WCA.

Climb, descent, and ETE

Climb planning comes from the POH performance chart — inputs are pressure altitude (departure and cruise) and OAT; outputs are time, distance, and fuel.

C172 sea level to 7,500 MSL on an ISA day → ~12 min, ~14 NM, ~1.5 gal.

Rule of thumb: 172 climbs ~700 FPM low, tapering to 400–500 FPM high.

Descent planning uses either time-based math or the 3-degree rule:

• Time-based: TOD distance = (altitude to lose / descent rate) × GS / 60
• 3-degree rule: 3 NM per 1,000 ft of descent

7,500 → 1,500 at 500 FPM, 110 KT GS → 12 min × 110/60 = 22 NM TOD. Same descent via 3° rule → 6,000 / 1,000 × 3 = 18 NM TOD. Either works for VFR.

Get ATIS at TOD − 5 NM.

ETE and ETA:

• ETE = distance / GS × 60 minutes (use leg GS, not TAS)
• ETA = departure time + ETE

110 NM at 100 KT GS → ETE = 66 min. Departing 1500Z → ETA 1606Z.

The fuel calculation

Total fuel required is the sum of five components plus a personal pad:

Total = taxi + climb + cruise + descent + reserve (+ personal pad)

Phase	Typical time	Typical 172 burn	Fuel
Taxi / run-up	12 min	1 gph	0.2 gal
Climb	12 min	7 gph	1.4 gal
Cruise (96 NM at 90 KT)	64 min	8 gph	8.5 gal
Descent	12 min	6 gph	1.2 gal
Subtotal flight			11.3 gal
Reserve (day, regulatory)	30 min	8 gph	4.0 gal
Personal pad	30 min	8 gph	4.0 gal
Total required			19.3 gal

The regulatory floor lives in §91.151:

• VFR day — fuel to first point of intended landing + 30 minutes at normal cruising speed
• VFR night — same + 45 minutes
• IFR has different rules (destination + alternate + 45 min, under a separate IFR fuel regulation)

Key nuance: reserve is calculated at the first point of intended landing — the destination. If you divert mid-flight, your "first point of intended landing" changes to the new alternate, and the reserve recomputes for the new geometry.

Planning for the unexpected

Real flights don't fly the plan. The recalculation discipline matters as much as the original computation.

Headwind is a multiplier

Headwind doesn't just slow you down — it scales total trip fuel because the same distance requires more time at the same burn rate.

200 NM leg, TAS 110, 8 gph cruise. Calm wind: 200 / 110 = 1.8 hr → 14.5 gal cruise. Same leg with 25 KT headwind: GS 85, 200 / 85 = 2.35 hr → 18.8 gal cruise. Cost: ~4 extra gallons. Plan for the worst forecast wind, not the average.

Recalculation scenarios

The DPE will hand you a scenario and watch you redo the math:

Scenario	What changes	What you recompute
Stronger headwind	GS → time → fuel	Trip fuel + compare to onboard
ATC vectors off route	Distance → time → fuel	Extra fuel for the deviation
Hold at destination	Hold time × burn rate	Add to total
Divert mid-flight	Distance + course + reserve location	Reserve at alternate, not original
Higher actual burn	Burn rate × all phases	Scale everything by burn ratio

Active monitoring

In flight, cross-check fuel state at every waypoint:

• Visual gauges every 5–10 minutes
• Calculated burn: time aloft × burn rate
• Cross-check the two — big mismatch means investigate
• At each waypoint: do I still have destination + reserve + personal pad?
• If "no," divert NOW while options exist

Personal fuel minimums

Set tighter than the regulatory floor:

• Day VFR — regulatory 30 + personal 30–60 = 60–90 min total
• Night VFR — regulatory 45 + personal 30–60 = 75–105 min total
• Marginal weather or remote terrain — add 30 min

State the specific number. "I plan to land with at least 8 gallons" beats "adequate reserve."

Worked examples:

• Stronger headwind than forecast. Original: 200 NM at 110 KT TAS, calm wind, GS 110, ETE 110 min, 14.7 gal cruise fuel. Actual: 25 KT headwind aloft. New GS = 85 KT, new ETE = 141 min, new cruise fuel = 18.8 gal. Difference: +4.1 gal. Add to total trip fuel + 30-min reserve. If new total exceeds usable (53 gal in a 172), divert plan. If close to usable, tighten landing minimums and watch fuel state. Walk the math out loud — don't just say "I'd recompute."
• Divert mid-flight. 50 NM short of destination KPRC, divert to KSEZ (25 NM south of KPRC; ~30 NM from current position). At 100 KT GS, the diversion leg is 18 min and ~2.4 gal. Add 30-min reserve at KSEZ — that's 4 gal. Total for diversion = 6.4 gal. Compare to onboard fuel at the decision point: 12 gal onboard = 5.6 gal margin (divert feasible); 7 gal onboard = 0.6 gal margin (too tight, find another alternate). Per §91.151, reserve is calculated at the first point of intended landing — after the divert decision that's KSEZ, not KPRC.